97 f250 5.8L starts to run rough and puffs out thick black smoke. It comes and goes. Any ideas?

Have you checked youre water level? White smoke can indicate water. May be headgasket. I would also dble check valv clearances and timing for tge rough running. 180° out of timing may be the rough running too.Just go through top to bottom your work. could be wires not in correct position.

Blue smoke is caused by oil. Rich running causes black smoke and will set the check engine light. Rich running (black smoke) on startup could be caused by a leaking injector. The blue smoke puff at startup is likely valve stem seals leaking or a bad crank case vent malfunction and sucking oil into the manifold at high vacuum conditions.

sounds like you have a blown head gasket.

Changing the plugs probably had nothing to do with it.
White smoke is usually a sign the engine is burning coolant or trans fluid. You might want to check those fluid levels.
If the coolant is low, you may have a leaking head gasket or intake gasket.

could be a stuck egr valve

Pull the vacuum hose off the fuel pressure regulator and if fuel runs out of it then replace the regulator.

Sounds like either the float level is too high, there is a problem with the float needle valve or the power valve is stuck. I'd take the carb off and either replace it or take it apart and check everything inside. If you do nothing, chances are it will either get worse or if it's a small piece of junk inside, it may clear up by itself...I'd take it apart. Since it's pretty new, if you are careful, likely you won't need a gasket kit.

antifreeze i think,heater matrix leak ,try putting a rad leak stopper in

white smoke is antifreeze try checking the compression

white smoke is water
blue smoke is oil.
nest time try and smell the white smoke see if it smells sweet?
if it does its antifreeze.
and also black smoke is fuel (like a leaky injector )
hope this helps
paul